Algebraic Surfaces and Holomorphic Vector Bundles

  title={Algebraic Surfaces and Holomorphic Vector Bundles},
  author={Robert Friedman},
1 Curves on a Surface.- Invariants of a surface.- Divisors on a surface.- Adjunction and arithmetic genus.- The Riemann-Roch formula.- Algebraic proof of the Hodge index theorem.- Ample and nef divisors.- Exercises.- 2 Coherent Sheaves.- What is a coherent sheaf?.- A rapid review of Chern classes for projective varieties.- Rank 2 bundles and sub-line bundles.- Elementary modifications.- Singularities of coherent sheaves.- Torsion free and reflexive sheaves.- Double covers.- Appendix: some… 

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